Math 143 C/E, Spring 2001
IPS Reading Questions
Chapter 5, Section 1 (pp. 372-385)

1. What is a population distribution of a variable? How does it differ from a sampling distribution? Does the distinction between a population that does exist (say, women between the ages of 18 and 24) and one that doesn't (all rods that would be produced by a certain manufacturing process if it continued forever) bother you?

   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

2. Compare Examples 5.2(b) and 5.3. The authors say emphatically that 5.2(b) is not a binomial setting, while 5.3 is “not quite a binomial setting.” Don't these scenarios seem similar? How do they justify letting it go in 5.3, but not in 5.2(b)? Do they indicate how you would decide whether a certain binomial setting is close enough to binomial to let it go?

   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

3. We have seen at least one probability histogram for a binomial distribution — Free-Throw Freddy and his 5 shots. The resulting histogram in that case was for B(5, 0.7), but recall that to get the appropriate probabilities from Table C, we had to look at B(5, 0.3). Select other values for n and p (ones that you can use Table C to get) and plot the resulting probability distribution B(n,p) until you feel confident you know what you're doing. Use this applet to compare your histograms to the correct answers.
4. Return to the binomial applet to experiment with it some more. Pick a value of p and stick with it while you vary the value of n. What do you notice about the center and spread of the distribution as you vary n? Does this seem to agree with what the formulas for mean and standard deviation tell you (see bottom of p. 380)?

   
   
   
   
   
   
   
   

5. In a binomial setting (see p. 376) where we assume samples of size n, the two most common random variables are the count of “successes” and the proportion of successes. What is the distinction between these two random variables? How are they related?